2. 1.1
ABC
ABC B
A C

3. AB
AC BC
2 2 2
C = A B

4. 1
ABC
C B
C
15
A
8
C

5. 2
C 2 2
= 8 + 15
= 64 + 225
= 289
= 17 x 17
= 17
C = 17
17

6. 2
b
1. b
2
2
2
2
2 2
2 = 1. 2 + b
b = 2 - 1.2

7. = 2.56
= 1.6 x 1.6
b = 1.6
1.6
1.1
1.

8. 1. 9 ,12 2. 11,60
2.
24
20
12
1. 7
2.

9. 3
12
1. 15
61
2.11

10. 1. 9,12
2 2 2
C = 12 + 9
= 144 + 81
= 225
2
= 15 x 15
C = 15
15

11. 2. 11, 60
C = 60 + 11
= 3,600 + 121
= 3,721
= 61 x 61
C = 61
61

12. 1. 20
12
2 2 2 2
a = c + b
2
a = 16
a = 20 + 12
16
2
= 400 - 144
= 256

13. 2.
7
24
2 2 2
C = 7+ 24
= 49 + 576
= 625
= 25 x 25
2
C = 25
25

14. 12
1.
15
2 2 2 2
B = c - b
B = 9
= 15 - 12
9
= 225 - 144
= 81

15. 2.
11
61
2 2 2
A = c - b
60
= 61 - 11
= 3,721 -121
= 3,600
2
= 60 x 60
A = 60

16. 13 1

17. =

18. A
c b
B a C
2 2 2
ABC AB = C
BC = a
AC = b c = a + b

19. DEF
EF D
DF a
b
b
DFE
E a F

20. 2 2 2
DEF DE = a +
b
2 2 2
ABC 2
c = a +b
2
DE = c
~
DE = c
DEF
= ABC . . .
DFE =
ACB = 90

21. Pythagoras of
Samos
580
-496

22. 55
Crotona

23. a
b

25. a
b

26. a
b
a
2.25
4 9.00
8
1 0
1. 9 8
9
4 2 0
= 2.250… 2 0
4

27. 5
9
1. = 0.555…
7
15
0.5
2. 50 = 0.4666…
33
0.46
11
37
3. - = - 1.515151…
-1.51

28. 1 4
1. 0.20
0.30
2.650
-1.83520
2.
1.18 , -2.327

29. 11
100
1 . 0.11=
137
1,000
2. - 0.137 =

30. 1 0.6
N = 0.6
N = 0.666…
1
1 x 10
1 x 10 10
1
2
10 N - N = 10 x

31. 2 10
2 1
-
10 N = 6.666… +
0.666…
9N = 6
2
N =6 1
9
0.6 = 6 2
9 3

32. 2 0.725
N = 0.725
1
N =
0.7252525…
1
x 1,000 2
1,000 N =
1000 x 0.7252525
1000 N =

33. 1 x 10
10 N = 10 x 0.7252525
… 3
10 N = 7.252525 ---
10
2
- 3
1000N - 10N =
725.2525… - 7.2525…
990N =

34. N = 718
990
0.725… = 718
990
718 990

36. 2.2
a
b
a b
b =0
1.23456789101121314…
3.4323223222…

39. 2.3
a
a
a

40. 7 49
7 = 49
-7 49
-7 = 49
a
a

41. 225
225 = 3x3x
5x5
2
= 5x
3 x 5x3
= 15 x

42. a
a
a

43. =
=-
=-
-

44. N =
N =
x ;
n = x
n =
x ;
n = x

45. – ;
n- n = ( )–
( )
n =
n =
=

46. =
=
=
=

47. =
=-
= -
-

48. =
=
=

49. =
=
=
=
=

50. =
x
ax + b = 0
a,b a≠0

51. x+ = x-
- x
(- x) x = (- x) x-
(- )x = (- )x -
- x = -
- x+ – =- –
- x=-
-
- x - = - -
x=

52. x x =
x–
( x ) =( x )-
= -
=
x
= x-

53. x= x
x x= x(
x )
x= x
x
x=
x=

54. x x
= x
x =(
x )
x =
=
x= x

55. - y =
(p- ) = p –
(y - )– ( y) =
x - (x - ) =
- x

56. -
-

58. -
x x x–
-
x (x - ) =-
x x- =-
(x x)- =-
x - =-
x =-

59. -
- -
= -
(-
) (- )=-
-
-
- -

60. x x,x x
x (x ) (x ) =
x x x =
(x x x) ( ) =
x =
x =
x =

61. ,
=
=
,

62. -

64. - ,- -
-

66. =
=

70. =

72. AE = DF

73. AE = DF

76. MB = NT

77. X

78. MB = NT
X=
X=